Loading and plotting data

Loading and plotting data#

This notebook showcases how to load and plot data that was previously generated using the creator.py script.

%load_ext autoreload
%autoreload 2

%matplotlib inline

The autoreload extension is already loaded. To reload it, use:
  %reload_ext autoreload

import xarray as xr
import matplotlib as mpl

from causaldynamics.scm import create_scm_graph
from causaldynamics.plot import animate_3d_trajectories, plot_trajectories, plot_scm

All relevant data is stored in a single dataset for easy access. Let’s load it and look at the content:

The data is stored in the Data variables. To get the data, e.g. the time_series, you can index it like a dictionary.

Let’s plot the time series.

root_nodes = ds["root_nodes"]
plot_trajectories(time_series, root_nodes=root_nodes, sharey=False, node_color="orange", root_node_color="dimgrey")

<xarray.plot.facetgrid.FacetGrid at 0x3339aca90>

../_images/746599b36dd4a925e52a1086dfa69e28ef91691182cec91ecd374eee1e3eddad.png

The adjacency matrix encodes the SCM graph structure. The first dimension are the incoming nodes and the second dimension are the outgoing nodes.

There is also a summary graph that additionally encodes the temporal nodes from at the root nodes, which drive the system.

Note: The adjacency_matrix_summary is especially relevant for causal discovery algorithms.

# You can access the underlying numpy array directly by calling .data
print(A.data)
# You can also convert it to a pandas DataFrame
print(A.to_dataframe())

[[0. 0. 0. 0. 0.]
 [1. 0. 0. 0. 0.]
 [1. 0. 0. 0. 0.]
 [1. 0. 0. 0. 0.]
 [1. 0. 0. 0. 0.]]
                  adjacency_matrix
node_in node_out                  
0       0                      0.0
        1                      0.0
        2                      0.0
        3                      0.0
        4                      0.0
1       0                      1.0
        1                      0.0
        2                      0.0
        3                      0.0
        4                      0.0
2       0                      1.0
        1                      0.0
        2                      0.0
        3                      0.0
        4                      0.0
3       0                      1.0
        1                      0.0
        2                      0.0
        3                      0.0
        4                      0.0
4       0                      1.0
        1                      0.0
        2                      0.0
        3                      0.0
        4                      0.0

Let’s visualize the graph

G = create_scm_graph(A.data)
plot_scm(G, root_nodes=root_nodes)

(<Axes: title={'center': 'Structural Causal Model'}>,
 {0: array([0.8812986, 0.9558141]),
  1: array([ 0.20354476, -0.10179732]),
  2: array([-0.94359961,  0.58761031]),
  3: array([-0.65000595, -0.4416271 ]),
  4: array([ 0.5087622, -1.       ])})

../_images/9ee7316abb8fb1690faaa17177e2e0ad267cb8852186a7bb8bbe28b02daabd62.png

# Creating an animation of the trajectories. 
# This may take a while to run...
mpl.rcParams["animation.embed_limit"] = 50 * 1024**2  # Increase the limit to 50MB

animate_3d_trajectories(time_series, 
                        root_nodes=root_nodes, 
                        plot_type="subplots",
                        frame_skip=5, 
                        rotation_speed=0.2, 
                        rotate=True, 
                        show_history=True, 
                        save_path=None, 
                        return_html_anim=True, # perfect for use in notebooks :)
                        show_plot=False,
                        root_node_alpha=0.5,
                        node_alpha=0.5,
                        linewidth=1.5)